Giant density fluctuations in semiconductors?

Abstract

Overhauser has pointed out that the lowest state of a one-dimensional Fermi gas is non-uniform in space. Here, we consider the possibility of obtaining such behavior in three-dimensional systems, which are made effectively one-dimensional by the application of large magnetic fields. The calculations are carried out in the Hartree-Fock approximation; they include estimates of the stability of the uniform ground state, and variational calculations to determine the nature of the non-uniform state when it exists. The uniform ground state is preferred in one-component plasmas since in them any density fluctuation automatically gives rise to charge fluctuations, which are energetically very costly. On the other hand, in multi-component plasmas, density fluctuations do not necessarily produce charge, and non-uniform ground states are likely. Multicomponent plasmas can be produced by doping many-valley semiconductors, or by injecting electrons and holes into simple ones. Several experimentally accessible examples of such plasmas are discussed.